Here the Hilbert-space-metric operator \(\Theta \) 
is precisely the one entering the
crypto-Hermiticity constraint (REF ).
In this context it is important to re-emphasize
that the choice of the metric \(\Theta \) 
only becomes admissible when one guarantees that
this operator is
self-adjoint in \({\cal H}_{math}\)  [1]}.
